Identify the set of the values of the real parameter \(d\) for which the following equation has no solution in \(\mathbb{R}\).
\[
x^{2} - 2dx + 2d^{2} - 9 = 0
\]
Identify the set of the values of the real parameter \(t\) for which the following equation has two different real roots.
\[
x^{2} + (t + 2)x + 1 = 0
\]
Find the values of real parameter \(p\)
which ensure that the following quadratic equation has solutions with nonzero
imaginary part.
\[
px^{2} + 4x - p + 5 = 0
\]